$J$ $K$ $L$ If: $ JK = 6x + 8$, $ JL = 46$, and $ KL = 3x + 2$, Find $KL$.
Answer: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {6x + 8} + {3x + 2} = {46}$ Combine like terms: $ 9x + 10 = {46}$ Subtract $10$ from both sides: $ 9x = 36$ Divide both sides by $9$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $KL$ $ KL = 3({4}) + 2$ Simplify: $ {KL = 12 + 2}$ Simplify to find ${KL}$ : $ {KL = 14}$